What is the equation for the line in slope-intercept form?

An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02

Increased Value is the amount obtained after deducting the Base Value from the current assessed value.

Given that,

An antique painting is purchased in 1980 for $995 = P

The value increases by 3.1% every = r

r = 3.1%

r = 3.1/100

r = 0.031

As we know,

Value of painting after t years: [tex]P (1+r)^t[/tex]

So, after 6 years:

f(6) = [tex]995 (1+0.031)^6[/tex]

or, f(6) = [tex]995 (1.031)^6[/tex]

or, f(6) = 1195.0197

or, f(6) = 1195.02

Now, at t = 0, f(0) = 995

Thus, value increased by, f(6) - f(0)

= [1195.02 - 995]

= 200.02

Thus, increase in price since it purchased = $200.02

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Answer:

Assuming you want to convert this to slope-intercept form.

Step-by-step explanation:

y=1/3x+3

Subtract 2x from both sides, then divide both sides by negative 6

if you want to graph it, this is what your graph should look like

** See attached photo**

Answer: 4/25

Step-by-step explanation:

(2/5)^2 or can write as 2/5 times 2/5

2/5 times 2/5 = 4/25

Answer:

0.08

Step-by-step explanation:

2/5 = 0.4 x 0.4

Answer:

72% of the trip is 169.2 miles

Step-by-step explanation:

[tex]\frac{235}{100} =\frac{y}{72}[/tex]

y · 100 = 235 · 72

100y = 16920

100y ÷ 100 = 16920 ÷ 100

y = 169.2

The volume of a solid of cylinder with a radius of 12 and a height of 24 is

3456[tex]\pi[/tex].

Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.

Given that the cylinder with a radius of 12 and a height of 24.

Volume of a cylinder = [tex]\pi[/tex] r² h

Volume of a cylinder = [tex]\pi[/tex] (12)² × 24

Volume of a cylinder = [tex]\pi[/tex] ( 144 × 24)

Volume of a cylinder =  [tex]\pi[/tex] (3456)

Therefore, the volume of cylinder is 3456[tex]\pi[/tex].

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Answer:

(y+1)³

Step-by-step explanation:

(y+1)⁵/(y+1)²

=(y+1)(y+1)(y+1)(y+1)(y+1)/(y+1)(y+1)

=(y+1)(y+1)(y+1)

=(y+1)³✓✓

The location of the transformed point will be at the coordinate (0,4).

In mathematics, a translation moves a shape left, right, up, or down but does not turn it. The translated (or picture) shapes appear to be the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Given that a point at (−3,−2) is transformed in two steps. It is reflected in y = x. It is translated as 3 units right and 2 units up.

The translated point will be,

(−3,−2) ⇒ (-3,2)

Translation of the point,

(-3,2) ⇒ (-3+3, 2+2) ⇒(0,4)

Therefore, the location of the transformed point will be at the coordinate (0,4).

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Answer:

2/5^4

Step-by-step explanation:

2/5 is being multiplied four times

The area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,pi]

What is a interval?

Given that:

x-axis on the interval [0,pi]

f(x) = sin x + 1

     = integral 0 - integral π (sin x) dx + integral 0 - integral π (1) dx

     = [- cos π + cos 0] + [π - 0]

     = [-(-1) + 1 ] + π

     = 2 + π

Therefore, the area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,π]

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Answer:

20.625

Step-by-step explanation:

a=− 3263i/24​ + 1/12 ​ ≈0.083333333−2.380111459i, b= 165/8 ​ =20.625

Hope this helps

Answer:

1.1

Step-by-step explanation:

Here is the answer. Have a good day!

each scarf's 0.4166 yards of blue scarf

This problem can be solved using a straightforward algebraic equation. For each scarf, Ayana requires many yards of blue cloth.

When solving a straightforward equation, visualize the equals symbol (=) as the fulcrum or center of a balance.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

In order to answer this question, let's say that each scarf needs x square inches of purple fabric and y square inches of blue fabric.

A total of six scarves are reportedly required. It is assumed that a total of 10 yards of fabric—the combined amount of the purple and the blue fabrics—will be utilized.

So that we may solve this equation.

We use x and y as 6x and 6y as 6 scarves are needed.

10 yards of cloth were used in total (6x + 6y).

Next up It goes without saying that 1 yard of purple cloth is required for each and every scarf.

Therefore, a total of 6 * 1(1/4) yards is required for 6 scarves.

As a result, 6x becomes 6 * 1/4 yards.

This equates to 6 yards of purple material

We now solve for the required amount of blue cloth.

6y = 10 -30/4  = 40-30/4 = 10/4

However, the yards are for six scarves, therefore we need to divide it by six to obtain the amount of material for one scarf.

Each scarf needs 0.4166 yards of blue fabric, or y = (10/4)/6 =10/4 *1/6 =10/24 = 5/12 yards.

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Answer:

c

Step-by-step explanation:

The correct order of sentences to bisect the angle Q is (1) draw a line from Q to where the arc crosses (2) vertex: set the compass to any convenient width (3) from where the arc crosses lag, make an arc.. (4) place the compass point on the angle Q.

We should know that an angle is the intersection of two or more straight lines.

In construction of angles, using the compass, the first thing is to locate a point say Q.  The open the leg of the compass to a convinient radius, make an arc at another point say P.  From the point P, bisect the initial arc so made then joion to the starting point Q.

Second, from the point where the arcs met on the two lines, make another two arcs above the points, then join them to the starting point Q

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Answer:

7, - 28 , 112 , - 448 , 1792

Step-by-step explanation:

to obtain a term in the sequence multiply the previous term by r , so

a₁ = 7

a₂ = a₁ × - 4 = 7 × - 4 = - 28

a₃ = a₂ × - 4 = - 28 × - 4 = 112

a₄ = a₃ × - 4 = 112 × - 4 = - 448

a₅ = a₄ × - 4 = - 448 × - 4 = 1792

Answer: A.

Step-by-step explanation: On the vertical number line, 2 1/5 is located below 2 3/5.

To compare the values of 2 1/5 and 2 3/5, you need to first convert them to fractions with a common denominator. For example, you can convert 2 1/5 to a fraction with a denominator of 5 by multiplying the numerator (1) and the denominator (5) by 2: 2 1/5 = (2 * 1)/(2 * 5) = 2/10 = 1/5.

Then, you can add the fractions to get a common denominator: 2 1/5 + 2 3/5 = (2 + 2) + (1/5 + 3/5) = 4 + (4/5) = 4 4/5.

Since 4 4/5 is greater than 4, it follows that 2 3/5 is greater than 2 1/5. Therefore, on the vertical number line, 2 3/5 is located above 2 1/5.

George is 17.55 cm taller than Alex. By simply subtracting the heights of the two, we get the required change between them.

Decimal subtraction is as similar to normal number subtraction. Here the subtraction starts from the decimals or the digits after the decimal point.

It is given that,

The height of George is 89.99 cm and the height of Alex is 72.44 cm.

Since 89.99 cm > 72.44 cm; George is taller than Alex.

To know how much he is taller, we just simply subtract the height of Alex from the height of George.

I.e., 89.99 cm - 72.44 cm = 17.55 cm

Therefore, George is 17.55 cm taller than Alex.

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In mathematics is an expression which is made up of variables and constants, along with algebraic operations

x = 1

3(5x+1) = 13x + 5

3(5x) + 3(1)

15x + 3 = 13x + 5        

-13x         -13x

2x + 3 = 5

 __-3__-3____

2x = 2

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one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]

and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]

and the roots of this polynomial is:

[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer:

x = 14.56 units

Step-by-step explanation:

When the coloured water evaporates and condenses on the inside of the top cup, there is no colour in the water on the inside surface of the cup.

As water molecules in the air cool, they slow down and combine into tiny droplets of liquid water. This process is called condensation. This happens when water molecules in the air touch the outside of a cold mug exposed to air.

Water vapour in the air is extracted by several techniques, such as cooling the air below the dew point, exposing the air to a desiccant, using membranes that allow only water vapour to pass, collecting the mist, or pressurizing the air. I can do it.

Common examples are water forming on the outside of a cold mug, or moisture forming on a car window on a cool night.

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Answer:

A=3, b=2, t=0 to t=5, covering 6 days. $3, $6, $12, $24, $48, $96.

Step-by-step explanation:

A is the starting amount at t=0. b is the base, two because the amount doubles each day. b would be 3 if it tripled every day. t is the final day number, counting from zero.

Answer: 55.5 as a fraction is 111/2.

Answer:

55.5/100 or 111/200 in its simplest form

Step-by-step explanation:

55.5 (per)cent) - means every 100

55.5/100= 111/200

Answer: The slope is 5/6

Answer:

5/6

Step-by-step explanation:

The adjacents angles are ∠ RTL and ∠ ETL, The obtuse vertical angles are ∠ RTL and ∠ STE, the two supplementary angles are ∠ NTE and

∠ NTR and angles supplementary to ∠ RTS is ∠ RTL

The two rays intersecting at a common point makes an angle.

Given is a figure,

Adjacent Angels =

The angles having one arm in common are called adjacent angles.

Here, adjacents angles are ∠ RTL and ∠ ETL

Vertical angles =

A pair of angles that have the same vertex and are on opposite sides of two intersecting rays makes Vertical angles

Here, vertical angles are ∠ RTL and ∠ STE

Supplementary angles =

When the sum of two angles is 180°, then they are supplementary angles.

Here, supplementary angles are ∠ NTE and ∠ NTR

We see that, the angle supplement to ∠ RTS is ∠ RTL

Hence, the correct answers are, adjacents angles = ∠ RTL and ∠ ETL, The obtuse vertical angles = ∠ RTL and ∠ STE, the two supplementary angles = ∠ NTE and ∠ NTR and angles supplementary to ∠ RTS is ∠ RTL

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Real estate is any immovable property of this kind that has a stake in a piece of land, a building, or housing in general. It also includes the natural resources on the land, such as water, crops, minerals, and minerals.

How does this occur?

from a company real estate broker's office. The competitor's sales were equal to the average number of sales 8 months before jured began gathering data and again 2 and 6 months after he began gathering data. The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.

Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.

Graph is given below in Image.

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Answer:

8

Step-by-step explanation:

The angle made between the two pieces of plywood found using the law of sines is approximately 85°

The law of sines states that the ratio of the sine of an angle to the length of the opposite side is the same for the three angles and sides of the triangle.

[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]

The length of one plywood = 7 feet

The angle made by the 7 feet plywood with the ground = 31°

Length of the other sheet of plywood = 4 feet

Using the law of sines, we get;

sin(31)/4 = sin(B)/7

sin(B) = 7 × (sin(31)/4)

∠B = arcsine(7 × (sin(31)/4)) ≈ 64.33°

The angle between the two pieces of wood is therefore;

Angle = 180° - 31° - 64.33° = 85°

The measure of the  angle formed between the two plywood is about 85°

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